details

property	value
status	complete
benchmark	apply.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	Mixed_HO_10

run statistics

property	value
solver	Wanda 2.2a
configuration	default
runtime (wallclock)	0.0790339 seconds
cpu usage	0.079269
user time	0.047293
system time	0.031976
max virtual memory	113188.0
max residence set size	3436.0

stage attributes

key	value
starexec-result	YES

output

YES We consider the system theBenchmark. Alphabet: cons : [a -> a * listf] --> listf dapply : [a * a -> a * a -> a] --> a lapply : [a * listf] --> a nil : [] --> listf Rules: dapply(x, f, g) => f (g x) lapply(x, nil) => x lapply(x, cons(f, y)) => f lapply(x, y) This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0). We use the dependency pair framework as described in [Kop12, Ch. 6/7], with static dependency pairs (see [KusIsoSakBla09] and the adaptation for AFSMs and accessible arguments in [FuhKop19]). We thus obtain the following dependency pair problem (P_0, R_0, computable, formative): Dependency Pairs P_0: 0] lapply#(X, cons(F, Y)) =#> lapply#(X, Y) Rules R_0: dapply(X, F, G) => F (G X) lapply(X, nil) => X lapply(X, cons(F, Y)) => F lapply(X, Y) Thus, the original system is terminating if (P_0, R_0, computable, formative) is finite. We consider the dependency pair problem (P_0, R_0, computable, formative). We apply the subterm criterion with the following projection function: nu(lapply#) = 2 Thus, we can orient the dependency pairs as follows: nu(lapply#(X, cons(F, Y))) = cons(F, Y) |> Y = nu(lapply#(X, Y)) By [FuhKop19, Thm. 61], we may replace a dependency pair problem (P_0, R_0, computable, f) by ({}, R_0, computable, f). By the empty set processor [Kop12, Thm. 7.15] this problem may be immediately removed. As all dependency pair problems were succesfully simplified with sound (and complete) processors until nothing remained, we conclude termination. +++ Citations +++ [FuhKop19] C. Fuhs, and C. Kop. A static higher-order dependency pair framework. In Proceedings of ESOP 2019, 2019. [Kop12] C. Kop. Higher Order Termination. PhD Thesis, 2012. [KusIsoSakBla09] K. Kusakari, Y. Isogai, M. Sakai, and F. Blanqui. Static Dependency Pair Method Based On Strong Computability for Higher-Order Rewrite Systems. In volume 92(10) of IEICE Transactions on Information and Systems. 2007--2015, 2009. popout

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